Violent relaxation was proposed half a century ago as responsible for non-collisional
dynamics in gravitationally bound systems of extended celestial objects after reaching an equilibrium {state that can be described thermodynamically}. It is based on a complete spatial exclusion {principle that formally leads} to a distribution function resembling the Fermi distribution.
We extend this theory to incomplete spatial exclusion by assuming that Fermi states can only be partially occupied. This is made possible by analogy to Fermi statistics. A new form of distribution function has been obtained. Formally it does not resemble the Fermi distribution. It consists of a difference of two Bose distributions but has the same properties as the Fermi distribution. Using it in the violent relaxation equation for the global gravitational {potential} extends the violent relaxation theory to incomplete exclusion. Though this refines violent relaxation theory, it does not resolve its basic deficiencies: the mass problem and those problems related to the mean field assumption.